These techniques are well known but one problem commonly encountered is that knowledge is required of the response of the array to signals arriving from different directions.
The set of complex responses across an array of n elements may be termed a point response vector (PRV) and the complete set of these vectors over all directions is known as the array manifold (of n dimensions). Normally a finite sampled form of the manifold is stored for use in the DF processing.
The (sampled) manifold can be obtained, in principle, either by calibration or by calculation or perhaps by a combination of these. Calibration, particularly over two angle dimensions (for example azimuth and elevation) is difficult and expensive, and calculation, particularly for arrays of simple elements, is much more convenient. In this case, if the positions of the elements are known accurately (to a small fraction of a wavelength, preferably less than 1%) the relative phases of a signal arriving from a given direction can be calculated easily, at the frequency to be used. The relative amplitudes should also be known as functions of direction, particularly for simple elements, such as monopoles or loops. If the elements are all similar and oriented in the same direction then the situation corresponds to one of equal, parallel pattern elements, and the relative gains across the set of elements are all unity for all directions.
The problem with calculating the array response is that this will not necessarily match the actual response for various reasons. One reason is that the signal may arrive after some degree of multipath propagation, which will distort the response. Another is that the array positions may not be specified accurately, and another that the element responses may not be as close to ideal as required. Nevertheless, in many practical systems these errors are all low enough to permit satisfactory performance to be achieved. However, one further source of error that it is important to eliminate, or reduce to a low level, is the matching of the channels between the elements and the points at which the received signals are digitized, and from which point no further significant errors can be introduced (FIG. 1). These channels should be accurately matched in phase and amplitude responses so that the signals when digitized are at the same relative amplitudes and phases as at the element outputs, and as given by the calculated manifold.
One solution to channel calibration is to feed an identical test signal into all the channels immediately after the elements. The relative levels and phases of these after digitization give directly the compensation (as the negative phase and reciprocal amplitude factor) which could be conveniently applied digitally to all signals before processing, when using the system (FIG. 2). This works well, but requires careful engineering to ensure the equality of the coupling and the accurate matching across the channels of the test signal, and may not be a feasible solution in all cases.
One problem which arises during the measurement of phase angles is that of ‘unwrapping’ the measured value. The indicated value will lie within a range having a magnitude of 360° (or 2π radians) with no indication of whether the true value equals this indicated value or includes a whole number multiple of 360°/2π radians. The term ‘unwrapping’ is used in the art to describe the process of resolving such indicated values to determine the true values.